Preheat the oven to 350 degrees. Fold a 16 inch long piece of foil to an 8x16 inch strip; place in a 8x8x2 inch baking pan, leaving overhang on 2 sides. Repeat with another sheet of foil in opposite direction, lining pan completely. Butter foil.
Place graham crackers in heavy-duty plastic bag. Using a rolling pin or mallet, crush crackers finely. Melt butter in a medium skillet over low heat. Remove from heat; add crumbs and toss to coat. Press crumbs evenly onto bottom of prepared pan. Bake crust until deep golden, about 12 minutes. Cool crust completely while preparing filling.
Using an electric mixer, beat cream cheese and sugar in a large bowl until smooth. Beat in egg and sour cream, then lemon juice, lemon peel and vanilla. Spread batter over crust.
Bake cheesecake until slightly puffed and set in center, about 30 minutes; cool completely in pan on rack. Chill cheesecake until cold, at least 2 hours. (Can be made 1 day ahead. Cover and keep chilled.).
Using foil overhang as aid, lift cheesecake from pan. Cut into 16 squares; arrange on platter. Top each square with berries. Chill until ready to serve, up to 3 hours. Serve Chilled.